Very numerous: all areas, especially Ulster and Connacht. An English name but more usually anglicisation of various indigenous names: Ó Cionga (L Ree); Mac Conraoi (Galway); Mac Fhearadhaigh (Oriel); Ó Maol Conaire (Roscommon); Ó Conraoi (Uí Maine) etc. An "umbrella" name, but based erroniously on the word rí, a king. IF & SGG.